ARTICLE IN PRESS
Computers & Geosciences 30 (2004) 523–532
The water color simulator WASI: an integrating software tool
for analysis and simulation of optical in situ spectra$
Peter Gege*
DLR, Remote Sensing Technology Institute, P.O. Box 1116, Wessling 82230, Germany
Received 11 August 2003; received in revised form 3 March 2004; accepted 12 March 2004
Abstract
A WINDOWS-based program was developed for modeling and analyzing optical in situ measurements in aquatic
environments. It supports eight types of spectra which are commonly measured by instruments on ship: downwelling
irradiance above and below the water surface, upwelling radiance above and below the surface, remote sensing
reflectance above and below the surface, irradiance reflectance, specular reflectance at the water surface, absorption,
attenuation, and bottom reflectance. These spectra can either be simulated (by forward calculation) or analyzed (by
inverse modeling) using well-established analytical models. The variability of a spectrum is determined by up to 25
parameters, depending on the spectrum type. All model constants and input spectra can be changed easily for
adaptation to a specific region. Effective methods are included for dealing with series of spectra. For some spectrum
types, inversion is a critical task and can produce erroneous results, that is when different parameter combinations
cause similar spectra. In order to handle this problem, specific inversion techniques are implemented for critical
spectrum types, and measures are included which allow fine-tuning of the fit procedure by the user.
r 2004 Elsevier Ltd. All rights reserved.
Keywords: Spectral measurements; Water; Analytical models; Inversion
1. Introduction
Optical sensors on ship provide many different types
of spectra: up- and downwelling radiance above and
below the surface, vector and scalar irradiance of the
upper and lower hemisphere in air and water, irradiance
reflectance, remote sensing reflectance, attenuation,
absorption, scattering, backscattering, and others.
Usually data from each instrument are analyzed with
software that is specifically tailored to that instrument or
spectrum type. However, operating a fleet of programs is
a potential source of errors, because the data analysis
programs must be consistent with each other concerning
the model and input data. In addition, maintenance and
data handling is time consuming, as is training new staff.
For these reasons it is desirable to have one single
integrating software. That was the motivation to
develop a comfortable, sensor-independent software
tool for forward and inverse calculations of major types
of spectra in aquatic environments which can be applied
for data analysis, data simulation, sensitivity studies,
and student training. The resulting ‘‘Water colour
Simulator’’ WASI is described in this article. It is
available as an executable program free of charge and
can be downloaded together with a user manual (Gege,
2002) from an ftp server.
2. Concept
2.1. General features
$
Code and manual available by anonymous ftp from http://
ftp.dfd.dlr.de in directory /pub/WASI.
*Fax: +49-8153-28-1444.
E-mail address: [email protected] (P. Gege).
WASI is designed as a sensor-independent spectra
generator and spectra analyzer with well-documented
calculation steps and automatic result visualization.
0098-3004/$ - see front matter r 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cageo.2004.03.005
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524
The supported spectrum types are listed in Table 1.
Forward calculation as well as inversion is implemented for all types, i.e. all spectra can be simulated
and analyzed. The variability of a spectrum is determined by up to 25 parameters, depending on the
spectrum type. A complete list of all 36 parameters is
given in Table 2.
All input and output files are in text format (ASCII),
making it easy to adapt the calculations to regional specifics by replacing some default input spectra
and changing material-specific constants. Spectral
data interval, number, and position of spectral channels are arbitrary: the spectra can either be calculated for equidistant wavelengths, or for arbitrary
spectral channels whose center wavelengths are
read from a text file. Spectral weighting within channels using sensor-specific response functions is not
supported.
WASI was developed for PC environments using
WINDOWS as the operating system. The programming
language is Borland Delphi 6. The program consists of
the executable file WASI.EXE, an initialization file
WASI.INI, and 25 input spectra. The input spectra are
listed in Table 3. Several input spectra and model
constants may be test-site specific. The data provided
with WASI were determined at Lake Constance (Gege,
1994, 1995; Heege, 2000), and are suited for calculating
all spectrum types of Table 1 at least from 390 to 800 nm
at a spectral resolution of 1 nm.
2.2. The file WASI.INI
All program settings are stored in ASCII format in a
single file, WASI.INI. It contains the file names of the
input spectra of Table 3, information on how to import
them (number of header lines, columns of x- and yvalues), input and output directories, model constants,
model parameter settings (default values, user values of
forward and inverse mode, range), settings concerning
program operation in the different modes, wavelength
range, spectral sampling interval, and visualization.
WASI.INI is automatically read during program
start. An update is created either manually during
program operation, when the user decides to store the
complete set of actual settings, or automatically at
program termination (optional). Whenever WASI creates output files, an updated copy of WASI.INI is
automatically stored in the relevant directory. Thus,
WASI.INI serves as the file which completely documents
all calculation settings.
WASI.INI is furthermore the key for other programs
to use WASI as a slave that generates or analyzes data
according to their inputs. For that, the master program
has to modify a copy of WASI.INI and it has to start
WASI using the syntax ‘WASI /INI-fileS’, where /
INI-fileS is a copy of WASI.INI containing the actual
settings. When WASI is started in this way, no user
interface is opened (background mode), and it automatically performs the sequence of reading /INI-fileS,
starting calculation as defined in that file, saving the
results, and terminating.
2.3. User interface
Table 1
Spectrum types and major model options
Spectrum type
Model options
Symbol Equation
Absorption
Exclude pure water
Include pure water
—
Wavelength
dependent
Constant
—
aWC(l)
a(l)
Kd(l)
Rsurf
rs (l)
(1)
(3)
(5)
(8a)
Rsurf
rs
R(l)
(8b)
(9)
Below surface
R–rs(l)
(11)
Above surface
For irradiance
sensors
For radiance sensors
Above surface
Rrs(l)
Rb(l)
(12)
(13)
Rbrs(l)
Ed(l)
(14)
(15)
Below surface
Below surface
E–d(l)
L–u(l)
(16)
(18)
Above surface
Lu(l)
(19)
Attenuation
Specular
reflectance
Irradiance
reflectance
Remote sensing
reflectance
Bottom
reflectance
Downwelling
irradiance
Upwelling
radiance
A representative screen shot of WASI’s graphical user
interface (GUI) is shown in Fig. 1. Some details depend
on the mode of operation and on the spectrum type. The
GUI consists of eight elements:
1. Drop-down list for selecting the spectrum type.
2. Check boxes for specifying the operation mode. The
box ‘‘invert spectra’’ selects between forward and
inverse mode. A hook in the ‘‘batch mode’’ check
box indicates that a series of spectra is analyzed;
otherwise, a single spectrum is inverted (single
spectrum mode). The check box ‘‘read from file’’
selects whether the spectra are read from files (hook),
or if previously forward calculated spectra are taken
(reconstruction mode, no hook).
3. Parameter list. This is the interface for the user to
specify parameter settings. All parameters relevant
for the selected spectrum type are tabulated. It
displays the parameters’ symbols (in WASI notation,
see Table 2), their values, and, in the inverse mode, a
check box for selecting whether a parameter is fitted
(hook) or kept constant during inversion (no hook).
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Table 2
Parameter list
Symbol
Ci
CL
CS
X
Y
S
n
T
f
Q
ysun
yv
sL
n
a
b
g
d
a
b
g
d
fn
WASI
C[i]
CL
CS
CX
CY
S
n
TW
f
Q
Sun
View
Sigma L
Nue
Alpha
Beta
Gamma
Delta
Alpha s
Beta s
Gamma s
Delta s
fA[n]
Units
1
mg l
mg l1
mg l1
m1
m1
nm1
—
C
—
sr
—
—
—
—
—
—
sr1
sr1
sr1
sr1
—
Description
Concentration of phytoplankton class No. i, i=0y5
Concentration of large suspended particles
Concentration of small suspended particles
Concentration of non-chlorophyllous particles
Concentration of Gelbstoff
Exponent of Gelbstoff absorption
Exponent of backscattering by small particles
Water temperature
Proportionality factor of reflectance (‘‘f-factor’’)
Anisotropy factor (‘‘Q-factor’’)
Sun zenith angle
Viewing angle (0=nadir)
Reflection factor of sky radiance
Exponent of aerosol scattering
Fraction of irradiance due to direct solar radiation
Fraction of irradiance due to molecule scattering
Fraction of irradiance due to aerosol scattering
Fraction of irradiance due to cloud scattering
Fraction of radiance due to direct solar radiation
Fraction of radiance due to molecule scattering
Fraction of radiance due to aerosol scattering
Fraction of radiance due to cloud scattering
Areal fraction of bottom surface type no. n, n=0y5
Table 3
Input spectra
Symbol
WASI
Units
Description
l
ai ðlÞ
aX ðlÞ
aY ðlÞ
aW(l)
daW(l)/dT
bL(l)
Ls(l)
Ed(l)
R(l)
an(l)
E0(l)
tA(l)
tC(l)
gi
x
aP[i]
aX
aY
aW
dadT
bL
Ls
Ed
R
albedo[n]
E0
tA
tC
gew
nm
m2 mg1
—
—
m1
m1 C1
—
mW m2 nm1 sr1
mW m2 nm1
—
—
mW m2 nm1
—
—
—
Wavelengths for which spectra are calculated
Specific absorption of phytoplankton class No. i, i=0y5
Normalized absorption of non-chlorophyllous particles
Normalized absorption of Gelbstoff
Absorption of pure water
Temperature gradient of pure water absorption
Normalized scattering of large suspended particles
Sky radiance
Downwelling irradiance above water surface
Irradiance reflectance
Albedo of bottom surface type no. n, n=0y5
Extraterrestrial solar irradiance
Transmission of the atmosphere for direct radiation
Transmission of clouds
Weights of channels at calculation of residuals
Which values are displayed depends on the mode of
operation: the actual values are shown in the forward
mode, the start values in the inverse mode, and the fit
results in the single spectrum mode of inversion.
4. The appearance of this area depends on the mode of
operation. In the forward and reconstruction mode, a
selection panel for specifying the iterations is
displayed (see Fig. 2). In the single spectrum mode
of inversion, the residuum and the number of
iterations are shown here after calculation is finished.
In the batch mode of inversion, this area is empty.
5. Check boxes for selecting model options. Several
spectrum types support options which further specify
the model, cf. Table 1. Each option is either switched
on or off.
6. Menu bar. Further details concerning the model, data
storage and visualization can be specified in various
pop-up windows, which are accessed via the menu bar.
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Fig. 1. Graphical user interface of WASI in inverse mode: 1—drop-down list for selecting the spectrum type, 2—check boxes for
specifying operation mode, 3—parameter list (model specific), 4—display elements depending on mode of operation, 5—check boxes
for selecting model options (model specific), 6—menu bar, 7—start button, and 8—plot window.
7. Start button. Calculation is started by pressing this
button.
8. Plot window. For visualization of imported and
calculated spectra. All input spectra of Table 3 can be
visualized. Calculated spectra are plotted automatically.
In the example of Fig. 1, a remote sensing reflectance
spectrum above water, imported from the file B1.fwd, was
inverted in the single spectrum mode. The spectrum had
been previously generated in the forward mode, where
noise with a standard deviation of 104 sr1 was added.
During inversion three parameters were fitted (C P, C L,
sigma L), the other parameters were kept constant. Fit
results are C P=1.91 mg l1, C L=1.98 mg l1, and
sigma L=0.00999. The fit converged after 86 iterations at
a residuum of 4.92 106 sr1.
3. Models
3.1. Absorption
3.1.1. Water constituents
Absorption of a mixture of water constituents is the
sum of the components’ absorption:
aWC ðlÞ ¼
5
X
i¼0
ðlÞ þ Ya ðlÞ:
Ci ai ðlÞ þ XaX
Y
ð1Þ
l denotes wavelength. Three groups of absorbing
water constituents are considered: phytoplankton, nonchlorophyllous particles, and Gelbstoff.
Phytoplankton: The high number of species that occur
in natural waters causes some variability of the
phytoplankton’s absorption properties. This is accounted for by the inclusion of six specific absorption
spectra ai ðlÞ: The default spectra provided with WASI
are taken from Gege (1998b). The ‘‘optical class’’
number 0 represents a mixture of various phytoplankton
species which can be considered typical for Lake
Constance. Thus, if no phytoplankton classification is
performed, the spectrum a0 ðlÞ is selected to represent
the specific absorption of phytoplankton. The Ci are the
pigment concentrations, where ‘‘pigment’’ is the sum of
chlorophyll-a and phaeophytin-a.
Non-chlorophyllous particles: Absorption is calculated
as product of concentration X and specific absorption
aX ðlÞ: The spectrum aX ðlÞ provided with WASI is taken
from Prieur and Sathyendranath (1981). It is normalized
to 1 at a reference wavelength l0 :
Gelbstoff (dissolved organic matter): Gelbstoff absorption is the product of concentration Y and specific
ðlÞ: The spectrum a ðlÞ can either be read
absorption aY
Y
from file or calculated using the usual exponential
approximation (Nyquist, 1979; Bricaud et al., 1981):
aY ðlÞ ¼ exp½Sðl l0 Þ;
ð2Þ
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where S denotes the spectral slope, and l0 is a reference
wavelength where aY is normalized to 1. Default values
are l0 ¼ 440 nm and S ¼ 0:014 nm1, which can be
considered representative of a great variety of water
types (Bricaud et al., 1981; Carder et al., 1989).
3.1.2. Natural water
The bulk absorption of a natural water body is the
sum of absorption of pure water and of the water
constituents:
daW ðlÞ
aðlÞ ¼ aW ðlÞ þ ðT T0 Þ
þ aWC ðlÞ:
ð3Þ
dT
Absorption of pure water is split up into a temperature-independent term aW ; which is valid for a reference
temperature T0 ; and a temperature gradient daW =dT
with T being the actual water temperature. For aW ðlÞ
the spectrum measured by Buiteveld et al. (1994) at
T0 ¼ 20 C is used for 391–787 nm, for daW ðlÞ=dT a
spectrum is provided which was measured by the author
(unpublished data).
3.2. Backscattering
Backscattering bb of a water body is the sum of
backscattering by pure water and suspended particles. In
WASI the following parameterization is chosen:
b ðlÞ ¼ b ðlÞ þ C b b ðlÞ þ C b ðl=l Þn :
ð4Þ
b
b;W
L b;L L
S b;S
S
For pure water, the empirical relation of Morel (1974)
is used: bb;W ðlÞ ¼ b1 ðl/l1 Þ4:32 : The specific backscattering coefficient, b1 ; depends on salinity. It is
b1 ¼ 0:00111 m–1 for fresh water and b1 ¼ 0:00144 m–1
for oceanic water with a salinity of 35–38%, when
l1 ¼ 500 nm is chosen as reference wavelength.
For suspended matter, a distinction between large
(\5 mm, index ‘‘L’’) and small (t5 mm, index ‘‘S’’)
particles is made. The backscattering of large particles is
calculated as the product of concentration CL ; specific
; and normalized scatterbackscattering coefficient bb;L
ing function bL ðlÞ: The user has several options for
calculation:
*
*
CL can be treated either as an independent parameter, or CL ¼ C0 can be set, where C0 is the
concentration of phytoplankton class No. 0 (see
Section 3.1.1). The latter is useful for Case 1 water
types where the concentrations of particles and
phytoplankton are highly correlated.
bb;L can be treated either as constant with a default
¼
value of 0.0086 m2 g–1 (Heege, 2000), or as bb;L
ACLB : Such a non-linear dependency of scattering on
concentration was observed for phytoplankton
(Morel, 1980). It may be used for Case 1 water
types, while b
b,L=constant is appropriate for Case 2
waters with significant sources of non-phytoplankton
suspended matter. Typical values of the empirical
*
527
constants are A ¼ 0:0006 m2 g–1 and B ¼ 0:37
(Sathyendranath et al., 1989).
bL(l) can either be read from file, or it can be
calculated as bL ðlÞ ¼ a0 ðlL Þ=a0 ðlÞ; where a0 ðlÞ is the
specific absorption spectrum of phytoplankton class
No. 0 (see Section 3.1.1), and lL denotes a reference
wavelength. This method assumes that backscattering by large particles originates mainly from phytoplankton cells, and couples absorption and scattering
according to Case 1 waters model of Sathyendranath
et al. (1989). However, such coupling may be used in
exceptional cases only, since living algae have a
negligible influence on the backscattering process by
oceanic waters (Ahn et al., 1992), and in Case 2
waters particle scattering is related to phytoplankton
absorption only weakly in general. In WASI, bL ðlÞ ¼
1 is set as default.
Backscattering by small particles is calculated as the
product of concentration CS ; specific backscattering
coefficient bb;S and a normalized scattering function
ðl=lS Þn : The exponent n depends on particle size
distribution and is typically in the order of 1
(Sathyendranath et al., 1989). bb;S in the order of
0.005 m2 g1 for lS ¼ 500 nm.
3.3. Attenuation
The diffuse attenuation coefficient of downwelling
irradiance (Ed ) is defined as Kd ¼ ð1=Ed Þ dEd =dz;
where z is the depth. It depends not only on the
properties of the medium, but also on the geometric
structure of the light field. The following parameterization of Kd is adapted from Gordon (1989), which
eliminates the light field effect near the surface to a large
extent:
Kd ðlÞ ¼ k0
aðlÞ þ bb ðlÞ
:
cos y0sun
ð5Þ
aðlÞ is calculated according to Eq. (3), bb ðlÞ using
Eq. (4). The coefficient k0 depends on the scattering
phase function. Gordon (1989) determined a value of
k0 ¼ 1:0395 from Monte Carlo simulations in Case 1
waters, Albert and Mobley (2003) found a value of k0 ¼
1:0546 from Hydrolight simulations in Case 2 waters.
Some authors use Eq. (5) with k0 ¼ 1 (Sathyendranath
and Platt, 1988, 1997; Gordon et al., 1975). In WASI, k0
is read from the WASI.INI file; the default value is
1.0546.
3.4. Specular reflectance
An above-water radiance sensor looking down to the
water surface measures the sum of two radiance
components: one from the water body, one from the
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surface. The radiance reflected from the surface, Lr ðlÞ; is
a fraction sL of sky radiance Ls ðlÞ:
Lr ðlÞ ¼ sL Ls ðlÞ:
ð6Þ
Ls ðlÞ is the average radiance of that area of the sky
that is specularly reflected into the sensor. It can be
imported from file or calculated using Eq. (17). sL is the
Fresnel reflectance and depends on the angle of
reflection. The value can either be specified by the user
or it can be calculated from the viewing angle yv using
the Fresnel equation for unpolarized light (Jerlov, 1976):
1sin2 ðyv y0v Þ tan2 ðyv y0v Þ
þ
sL ¼ 2
ð7Þ
:
2sin ðyv þ y0v Þ tan2 ðyv þ y0v Þ
y0v is the angle of refraction, which is related to yv by
Snell’s law nW sin y0v ¼ sin yv ; where nW E1:33 is the
refractive index of water. For viewing angles near nadir,
sL E0:02:
The ratio of the radiance reflected from the water
surface to the downwelling irradiance,
Rsurf
rs ðlÞ ¼
Lr ðlÞ
Ls ðlÞ
¼ sL
;
Ed ðlÞ
Ed ðlÞ
ð8aÞ
is called specular reflectance. Ed ðlÞ and Ls ðlÞ can either
be imported from file, or one or both can be calculated
using Eq. (15) or (17). If the wavelength-independent
model of surface reflection is chosen, it is
sL
Rsurf
:
ð8bÞ
rs ¼
p
Toole et al. (2000) showed that Rsurf
rs ðlÞ is nearly
spectrally flat at overcast sky, but clearly not for clearsky conditions. Thus, Eq. (8a) should be used in general,
and Eq. (8b) at most for days with overcast sky.
3.5. Irradiance reflectance
The ratio of upwelling irradiance to downwelling
irradiance in water, RðlÞ ¼ Eu ðlÞ=Ed ðlÞ; is called
irradiance reflectance (Mobley, 1994). A suitable parameterization in terms of absorption aðlÞ and backscattering bb ðlÞ was found by Gordon et al. (1975):
RðlÞ ¼ f
bb ðlÞ
:
aðlÞ þ bb ðlÞ
ð9Þ
Independently, Prieur (1976) found the relation
RðlÞ ¼ f 0 bb ðlÞ=aðlÞ: Both relations are implemented in
WASI. The Gordon algorithm (9) is set as default,
because it restricts the R=f values to the physically
reasonable range from 0 to 1, which is not the case for
the Prieur equation.
The factor f depends on the scattering properties
of the water and on the geometric structure of the
light field. It can be treated either as an independent parameter with a default value of 0.33, or the
relationship of Albert and Mobley (2003) can be used:
f ¼ 0:1034ð1 þ 3:3586ob 6:5358o2b
2:4121
;
þ 4:6638o3b Þ 1 þ
0
cos ysun
ð10Þ
where ob ¼ bb =ða þ bb Þ and y0sun is the sun zenith angle
in water. Also parameterizations of Kirk (1984), Morel
and Gentili (1991), and Sathyendranath and Platt (1997)
are implemented in WASI and can be selected.
3.6. Remote sensing reflectance
The ratio of upwelling radiance to downwelling
irradiance, Rrs ðlÞ ¼ Lu ðlÞ=Ed ðlÞ; is called remote sensing reflectance (Mobley, 1994). In water, it is proportional to RðlÞ:
R
rs ðlÞ ¼
RðlÞ
:
Q
ð11Þ
The factor of proportionality, Q ¼ Eu =L
u ; is a
measure for the anisotropy of the upwelling light field
and typically in the order of 5 sr. It is treated as a
wavelength-independent parameter. Alternately to
Eq. (11), the equation R
rs ðlÞ ¼ frs ob ðlÞ can be selected,
where frs ¼ f =Q is parameterized similarly to Eq. (10) as
a function of ob ; y0sun ; and the viewing angle in water, y0v
(Albert and Mobley, 2003).
In air, the remote sensing reflectance is related to RðlÞ
as follows (Mobley, 1994):
Rrs ðlÞ ¼
ð1 sÞð1 s
RðlÞ
LÞ
þ Rsurf
rs ðlÞ:
n2w Q
1 s RðlÞ
ð12Þ
The first term describes reflection in the water, the
second at the surface. Frequently, the first term alone is
called remote sensing reflectance (e.g. Mobley, 1994). In
WASI, the reflection at the surface is also included in the
Rrs definition. It is calculated using Eq. (8a) or (8b) and
can easily be excluded by setting sL equal to zero.
Two alternate equations for calculating Rrs ðlÞ are also
implemented in WASI. The first links remote sensing in
water to that in air: in numerator and denominator of
Eq. (12) RðlÞ is replaced by QR
rs ðlÞ: The second avoids
the use of the factor Q; which is difficult to assess: in the
numerator RðlÞ is replaced by QR
rs ðlÞ:
The factors s
L ; s; and s are the reflection factors for
L
u ; Ed ; and Eu ; respectively. sL can either be calculated
as a function of yv using Eq. (7), or a constant value can
be taken. s depends on the radiance distribution and on
surface waves. Typical values are 0.02–0.03 for clear sky
conditions and solar zenith angles below 45 , and 0.05–
0.07 for overcast skies (Jerlov, 1976; Preisendorfer and
Mobley, 1985, 1986). s is in the range of 0.50–0.57 with
a value of 0.54 being typical (Jerome et al., 1990;
Mobley, 1999). Default values are s ¼ 0:03; s
L ¼ 0:02;
s ¼ 0:54; Q ¼ 5 sr, and nW ¼ 1:33:
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3.7. Bottom reflectance
The irradiance reflectance of a surface is called albedo.
When N different surfaces of albedo an ðlÞ are viewed
simultaneously, the measured albedo is the following
sum:
Rb ðlÞ ¼
N1
X
fn an ðlÞ:
ð13Þ
n¼0
fn is the areal fraction of surface
number n within the
P
sensor’s field of view; it is
fn ¼ 1: This equation is
implemented in WASI for N ¼ 6 bottom types.
When the upwelling radiation is measured by a
radiance sensor, the corresponding remote sensing
reflectance can be expressed as follows:
Rbrs ðlÞ ¼
N1
X
fn Bn an ðlÞ:
ð14Þ
529
two provided with WASI were determined from
measurements at Lake Constance.
The downwelling irradiance in water, Ed ; is related to
the downwelling irradiance in air, Ed ; through Ed ðlÞ ¼
ð1 sÞEd ðlÞ þ s Eu ðlÞ: s is the reflection factor for
downwelling irradiance in air, s for upwelling irradiance in water, and Eu is the upwelling irradiance in
water. Using the irradiance reflectance R ¼ Eu =Ed
yields the following expression:
Ed ðlÞ ¼
1s
Ed ðlÞ:
1 s RðlÞ
ð16Þ
This equation is used in WASI for calculating Ed ðlÞ:
RðlÞ is calculated using Eq. (9). Ed ðlÞ can either be
calculated according to Eq. (15), or a measured spectrum can be taken. Default values of the reflection
factors are s ¼ 0:03 and s ¼ 0:54:
n¼0
Bn is the proportion of radiation which is reflected
into the direction of the sensor. In WASI, the Bn ’s of all
surfaces are assumed to be angle-independent. The
default values are set to Bn ¼ 1=p ¼ 0:318 sr1, which
represents isotropic reflection (Lambertian surfaces).
The same parameterization as for Ed ðlÞ is also
implemented for Ls ðlÞ:
Ls ðlÞ ¼ ½a tA ðlÞ þ b ðl=lR Þ4:09 þ g ðl=lM Þn
þ d t ðlÞE ðlÞ:
C
3.8. Downwelling irradiance
An analytic model of the downwelling irradiance
spectrum Ed ðlÞ with only few parameters was developed
by Gege (1994, 1995). It fits to measured spectra with a
high degree of accuracy (average rms error of 0.1%).
The radiation illuminating the water surface is parameterized as the sum of four spectrally different
components: (1) the direct solar radiation transmitted
through the atmosphere, (2) the blue sky, (3) radiation
scattered by aerosols, and (4) clouds. Each component is
expressed in terms of a wavelength-dependent fraction
of the extraterrestrial solar irradiance E0 ðlÞ:
Ed ðlÞ ¼ ½atA ðlÞ þ bðl=lR Þ4:09 þ gðl=lM Þn
þ dtC ðlÞE0 ðlÞ:
3.9. Sky radiance
ð15Þ
The four functions ti(l)={tA(l), (l/lR)4.09, (l/lM)n,
tC(l)} are transmission spectra which spectrally characterize the four light sources. Their weights a; b; g; d
may change from one measurement to the next, but the
ti ðlÞ themselvesRare assumed to be
R constant. Each ti ðlÞ is
normalized as ti ðlÞE0 ðlÞ dl ¼ E0 ðlÞ dl; the integration interval is set to 400–800 nm by default.
The functions (l=lR )4.09 and (l=lM )n are calculated
during run-time. Normalization yields their scaling
factors: lR ¼ 533 nm, and lM is typically between
563 nm (n ¼ 1) and 583 nm (n ¼ 1). The exponent n
parameterizes the wavelength dependency of aerosol
scattering. The two other functions, tA ðlÞ and tC ðlÞ; are
read from file. After import they are normalized. The
0
ð17Þ
The functions E0 ðlÞ; tA ðlÞ; ðl=lR Þ4:09 ; ðl=lM Þn ; and
tC ðlÞ are those of Eq. (15). Parameters of Ls ðlÞ are the
weights a ; b ; g ; d ; which represent the relative
intensities of the four above-mentioned light sources for
a radiance sensor, and the exponent n:
This model of Ls ðlÞ has been included for modeling
specular reflection at the water surface. Its usefulness
has been demonstrated (Gege, 1998a). Capillary waves
at the water surface, and moreover gravity waves, spread
greatly the sky area that is reflected into a radiance
sensor, and change the angle of reflection. Consequently,
measurements of Ls ðlÞ are frequently not representative.
For these cases, and if no Ls ðlÞ measurement is
available, Eq. (17) can be applied. If the wavelengthindependent model of surface reflection is chosen,
Ls ðlÞ ¼ Ed ðlÞ=p is set.
3.10. Upwelling radiance
The upwelling radiance is that part of the downwelling irradiance which is reflected back from the water
into a down-looking radiance sensor. Calculation is
based on a model of Rrs and a model or a measurement
of Ed :
In water, Eq. (16) is used for calculating Ed ðlÞ; and
Eq. (11) for R
rs ðlÞ: The upwelling radiance is then
calculated as follows:
L
u ðlÞ ¼ Rrs ðlÞEd ðlÞ:
ð18Þ
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530
In air, the upwelling radiance after crossing the waterair boundary is related to L
u as follows:
1 s
L Lu ðlÞ ¼
Lu ðlÞ þ Lr ðlÞ:
n2W
ð19Þ
The first term on the right-hand side is the radiance
upwelling in the water, weakened at the interface by
Fresnel reflection (factor 1 s
L ) and refraction (flux
dilution by widening of the solid angle, factor 1=n2w ).
L
u ðlÞ is obtained from Eq. (18), Lr ðlÞ from Eq. (6). sL
can either be calculated as a function of yv using Eq. (7),
or a constant value can be taken. Default values of the
constants are s
L ¼ 0:02 and nW ¼ 1:33:
5. Inverse modeling
Inverse modeling is the determination of model
parameters for a given spectrum. Table 2 summarizes
all parameters whose values can principally be determined via fit. The actual number of fit parameters
depends on the spectrum type, on model options, and on
the user’s choice which parameters to fit and which to fix
during inversion. Three modes of operation are implemented:
*
4. Forward modeling
Forward modeling is the calculation of spectra
according to user-specified parameter settings. During
a run, either a single spectrum or a series of spectra is
calculated. For calculating a series of spectra, up to
three parameters from Table 2 can be iterated simultaneously. The iterated parameters, their range of variation, and the number of steps are specified using the
selection panel shown in Fig. 2. In the forward mode,
this panel is always displayed in the main window (as
element number 4 of Fig. 1). The check boxes labeled
‘‘log’’ specify whether the parameter intervals are
equidistant on a linear scale (no hook) or on a
logarithmic scale (hook).
The calculated spectra are automatically plotted on
screen, and can be saved as individual files in ASCII
format. Two features are implemented which are useful
for performing sensor-specific simulations:
*
*
Gaussian distributed noise
has to specify the standard
The radiometric dynamics
realised by user-specified
spectral values.
can be added. The user
deviation.
can be reduced. This is
rounding of calculated
Fig. 2. Selection panel for specifying parameter iteration at
forward calculation.
*
*
Single spectrum mode. Fitting is performed for a
single spectrum which the user loads from file. After
inversion, an overlay of imported spectrum and fit
curve is automatically shown on screen and resulting
fit values, number of iterations, and residuum are
displayed. This mode allows to inspect the fit results
of individual measurements. It is useful for optimizing the choice of initial values and the fit strategy
before starting a batch job.
Batch mode. A series of spectra from file is fitted.
After each inversion, an overlay of imported
spectrum and fit curve is automatically shown on
screen. This mode is useful for processing large data
sets.
Reconstruction mode. Combines forward and inverse
modes. Inversion is performed for a series of forward
calculated spectra which are not necessarily read
from file. The model parameters can be chosen
differently for forward and inverse calculations. This
mode is useful for performing sensitivity studies.
The fit parameters are determined iteratively: in the
first iteration, a model spectrum is calculated using
initial values for the fit parameters. This model spectrum
is compared with the measured spectrum by calculating
the residuum as a measure of correspondence. Then, in
the further iterations, the values of the fit parameters are
altered, resulting in altered model curves and altered
residuals. For selecting a new set of parameter values
from the previous sets, the Simplex algorithm is used
(Nelder and Mead, 1965; Caceci and Cacheris, 1984).
The procedure is stopped after the best fit between
calculated and measured spectrum has been found,
which corresponds to the minimum residuum. The
values that were used in the step with the smallest
residuum are the results.
If the solution of the inversion problem is ambiguous,
the inversion algorithm may not find the correct values
of the fit parameters. The problem occurs when different
sets of model parameters yield similar spectra, i.e. the
problem is model specific. Measures are implemented in
WASI to handle the ambiguity problem. The most
effective measure is to use ‘‘realistic’’ values of all fit
parameters as initial values when inversion is started.
Methods are implemented to determine automatically
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P. Gege / Computers & Geosciences 30 (2004) 523–532
start values of some parameters. Other fit tuning
measures are to restrict the search to the expected
range, or to weight the spectral information differently
for individual spectral channels. The description and
discussion of these measures is out of scope of this
article. A paper focusing on the inversion subject is in
preparation; some details are also described in the
manual (Gege, 2002).
6. Conclusions
The Water Colour Simulator, WASI, is a software
which integrates forward and inverse modeling for eight
common types of optical in situ measurements in aquatic
environments. It is designed for effectively generating,
analyzing, and visualizing series of spectra. Computing
is fast: for example, 0.17 s per spectrum were required on
average using a 450 MHz Pentium III notebook for
determining the concentrations C0 ; CL and Y from 1331
irradiance reflectance spectra by inverse modeling of 300
channels (Gege, 2003).
The focus of the implemented models is on measurements in deep water. In addition, models for the
illumination (downwelling irradiance, sky radiance)
and for linear combinations of reflectance spectra
(bottom reflectance) are included. Algorithms for
shallow water applications have been developed recently
(Albert and Mobley, 2003). Their implementation in
WASI is in progress. For the future it is planned to
account for physical effects which are so far ignored
(fluorescence, Raman scattering), and to cope with
vertical profiles.
References
Ahn, Y.H., Bricaud, A., Morel, A., 1992. Light backscattering
efficiency and related properties of some phytoplankton.
Deep-Sea Research 39 (11/12), 1835–1855.
Albert, A., Mobley, C.D., 2003. An analytical model for
subsurface irradiance and remote sensing reflectance in
deep and shallow case-2 waters. Optics Express 11 (22),
2873–2890.
Bricaud, A., Morel, A., Prieur, L., 1981. Absorption by
dissolved organic matter of the sea (yellow substance) in
the UV and visible domains. Limnology and Oceanography
26 (1), 43–53.
Buiteveld, H., Hakvoort, J.H.M., Donze, M., 1994. The optical
properties of pure water. In: Proceedings Ocean Optics XII,
SPIE, Vol. 2258. pp. 174–183.
Caceci, M.S., Cacheris, W.P., 1984. Fitting curves to data. Byte
340–362.
Carder, K.L., Steward, R.G., Harvey, G.R., Ortner, P.B., 1989.
Marine humic and fulvic acids: their effects on remote
sensing of ocean chlorophyll. Limnology and Oceanography
34 (1), 68–81.
531
Gege, P., 1994. Gewässeranalyse mit passiver Fernerkundung:
Ein Modell zur Interpretation optischer Spektralmessungen.
Dissertation, DLR-Forschungsbericht 94-15, 171pp.
Gege, P., 1995. Water analysis by remote sensing: a model for
the interpretation of optical spectral measurements. Technical Translation ESA-TT-1324, July 1995, 231pp.
Gege, P., 1998a. Correction of specular reflections at the water
surface. In: Proceedings Ocean Optics XIV, 10–13 November 1998, Conference Papers, Vol. 2. Kailua-Kona, Hawaii,
USA.
Gege, P., 1998b. Characterization of the phytoplankton in
Lake Constance for classification by remote sensing. In:
Bäuerle, E., Gaedke, U. (Eds.), Lake Constance—Characterization of an ecosystem in transition. Archiv für
Hydrobiologie, special issues: Advances in Limnology 53,
179–193.
Gege, P., 2002. The Water Colour Simulator WASI. User
manual for version 2. DLR Internal Report IB 564-01/02,
60pp.
Gege, P., 2003. Wasi—a software tool for water spectra.
Backscatter 14 (1), 22–24.
Gordon, H.R., 1989. Can the Lambert–Beer law be applied to
the diffuse attenuation coefficient of ocean water? Limnology and Oceanography 34 (8), 1389–1409.
Gordon, H.R., Brown, O.B., Jacobs, M.M., 1975. Computed
relationships between the inherent and apparent optical
properties of a flat homogeneous ocean. Applied Optics 14
(2), 417–427.
Heege, T., 2000. Flugzeuggestützte Fernerkundung von Wasserinhaltsstoffen im Bodensee. Dissertation, DLR-Forschungsbericht 2000-40, 141pp.
Jerlov, N.G., 1976. Marine Optics. Elsevier Scientific
Publishing Company, Amsterdam, The Netherlands
231pp.
Jerome, J.H., Bukata, R.P., Bruton, J.E., 1990. Determination
of available subsurface light for photochemical and photobiological activity. Journal of Great Lakes Research 16 (3),
436–443.
Kirk, J.T.O., 1984. Dependence of relationship between
inherent and apparent optical properties of water on
solar altitude. Limnology and Oceanography 29 (2),
350–356.
Mobley, C.D., 1994. Light and Water. Academic Press, San
Diego 592pp.
Mobley, C.D., 1999. Estimation of the remote-sensing reflectance from above-surface measurements. Applied Optics 38
(36), 7442–7455.
Morel, A., 1974. Optical properties of pure water and pure
sea water. In: Jerlov, N.G., Steemann, N.E. (Eds.), Optical Aspects of Oceanography. Academic Press, London,
pp. 1–24.
Morel, A., 1980. In water and remote measurements of ocean
colour. Boundary-Layer Meteorology 18, 177–201.
Morel, A., Gentili, B., 1991. Diffuse reflectance of oceanic
waters: its dependence on Sun angle as influenced by the
molecular scattering contribution. Applied Optics 30 (30),
4427–4438.
Nelder, J.A., Mead, R., 1965. A simplex method for function
minimization. Computer Journal 7, 308–313.
Nyquist, G., 1979. Investigation of some optical properties of
seawater with special reference to lignin sulfonates and
ARTICLE IN PRESS
532
P. Gege / Computers & Geosciences 30 (2004) 523–532
humic substances. Dissertation, Göteborgs Universitet,
200pp.
Preisendorfer, R.W., Mobley, C.D., 1985. Unpolarized irradiance reflectances and glitter patterns of random capillary
waves on lakes and seas by Monte Carlo simulation. NOAA
Technical Memorandum ERL PMEL-63, Pacific Marine
Environment Laboratory, Seattle, WA, 141pp.
Preisendorfer, R.W., Mobley, C.D., 1986. Albedos and glitter
patterns of a wind-roughened sea surface. Journal of
Physical Oceanography 16 (7), 1293–1316.
Prieur, L., 1976. Transfers radiatifs dans les eaux de mer.
Dissertation, Doctorat d’Etat, Université Pierre et Marie
Curie, Paris, 243pp.
Prieur, L., Sathyendranath, S., 1981. An optical classification of
coastal and oceanic waters based on the specific spectral
absorption curves of phytoplankton pigments, dissolved
organic matter, and other particulate materials. Limnology
and Oceanography 26 (4), 671–689.
Sathyendranath, S., Platt, T., 1988. Oceanic primary production: estimation by remote sensing at local and regional
scales. Science 241, 1613–1620.
Sathyendranath, S., Platt, T., 1997. Analytic model of ocean
color. Applied Optics 36 (12), 2620–2629.
Sathyendranath, S., Prieur, L., Morel, A., 1989. A threecomponent model of ocean colour and its application to
remote sensing of phytoplankton pigments in coastal waters.
International Journal of Remote Sensing 10 (8), 1373–1394.
Toole, D.A., Siegel, D.A., Menzies, D.W., Neumann, M.J.,
Smith, R.C., 2000. Remote-sensing reflectance determinations in the coastal ocean environment: impact of instrumental characteristics and environmental variability.
Applied Optics 39 (3), 456–469.